Update nitrokey crate to 0.4.0

This change finally updates the version of the nitrokey crate that we
consume to 0.4.0. Along with that we update rand_core, one of its
dependencies, to 0.5.1. Further more we add cfg-if in version 0.1.10 and
getrandom in version 0.1.13, both of which are now new (non-development)
dependencies.

Import subrepo nitrokey/:nitrokey at e81057037e9b4f370b64c0a030a725bc6bdfb870
Import subrepo cfg-if/:cfg-if at 4484a6faf816ff8058088ad857b0c6bb2f4b02b2
Import subrepo getrandom/:getrandom at d661aa7e1b8cc80b47dabe3d2135b3b47d2858af
Import subrepo rand/:rand at d877ed528248b52d947e0484364a4e1ae59ca502

1 files changed, 329 insertions, 0 deletions

diff --git a/rand/rand_distr/src/binomial.rs b/rand/rand_distr/src/binomial.rs
new file mode 100644
index 0000000..0e6bf9a
--- /dev/null
+++ b/rand/rand_distr/src/binomial.rs
@@ -0,0 +1,329 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2016-2017 The Rust Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! The binomial distribution.
+
+use rand::Rng;
+use crate::{Distribution, Uniform};
+
+/// The binomial distribution `Binomial(n, p)`.
+///
+/// This distribution has density function:
+/// `f(k) = n!/(k! (n-k)!) p^k (1-p)^(n-k)` for `k >= 0`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Binomial, Distribution};
+///
+/// let bin = Binomial::new(20, 0.3).unwrap();
+/// let v = bin.sample(&mut rand::thread_rng());
+/// println!("{} is from a binomial distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+pub struct Binomial {
+    /// Number of trials.
+    n: u64,
+    /// Probability of success.
+    p: f64,
+}
+
+/// Error type returned from `Binomial::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `p < 0` or `nan`.
+    ProbabilityTooSmall,
+    /// `p > 1`.
+    ProbabilityTooLarge,
+}
+
+impl Binomial {
+    /// Construct a new `Binomial` with the given shape parameters `n` (number
+    /// of trials) and `p` (probability of success).
+    pub fn new(n: u64, p: f64) -> Result<Binomial, Error> {
+        if !(p >= 0.0) {
+            return Err(Error::ProbabilityTooSmall);
+        }
+        if !(p <= 1.0) {
+            return Err(Error::ProbabilityTooLarge);
+        }
+        Ok(Binomial { n, p })
+    }
+}
+
+/// Convert a `f64` to an `i64`, panicing on overflow.
+// In the future (Rust 1.34), this might be replaced with `TryFrom`.
+fn f64_to_i64(x: f64) -> i64 {
+    assert!(x < (::std::i64::MAX as f64));
+    x as i64
+}
+
+impl Distribution<u64> for Binomial {
+    #[allow(clippy::many_single_char_names)]  // Same names as in the reference.
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        // Handle these values directly.
+        if self.p == 0.0 {
+            return 0;
+        } else if self.p == 1.0 {
+            return self.n;
+        }
+
+        // The binomial distribution is symmetrical with respect to p -> 1-p,
+        // k -> n-k switch p so that it is less than 0.5 - this allows for lower
+        // expected values we will just invert the result at the end
+        let p = if self.p <= 0.5 {
+            self.p
+        } else {
+            1.0 - self.p
+        };
+
+        let result;
+        let q = 1. - p;
+
+        // For small n * min(p, 1 - p), the BINV algorithm based on the inverse
+        // transformation of the binomial distribution is efficient. Otherwise,
+        // the BTPE algorithm is used.
+        //
+        // Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1988. Binomial
+        // random variate generation. Commun. ACM 31, 2 (February 1988),
+        // 216-222. http://dx.doi.org/10.1145/42372.42381
+
+        // Threshold for prefering the BINV algorithm. The paper suggests 10,
+        // Ranlib uses 30, and GSL uses 14.
+        const BINV_THRESHOLD: f64 = 10.;
+
+        if (self.n as f64) * p < BINV_THRESHOLD &&
+           self.n <= (::std::i32::MAX as u64) {
+            // Use the BINV algorithm.
+            let s = p / q;
+            let a = ((self.n + 1) as f64) * s;
+            let mut r = q.powi(self.n as i32);
+            let mut u: f64 = rng.gen();
+            let mut x = 0;
+            while u > r as f64 {
+                u -= r;
+                x += 1;
+                r *= a / (x as f64) - s;
+            }
+            result = x;
+        } else {
+            // Use the BTPE algorithm.
+
+            // Threshold for using the squeeze algorithm. This can be freely
+            // chosen based on performance. Ranlib and GSL use 20.
+            const SQUEEZE_THRESHOLD: i64 = 20;
+
+            // Step 0: Calculate constants as functions of `n` and `p`.
+            let n = self.n as f64;
+            let np = n * p;
+            let npq = np * q;
+            let f_m = np + p;
+            let m = f64_to_i64(f_m);
+            // radius of triangle region, since height=1 also area of region
+            let p1 = (2.195 * npq.sqrt() - 4.6 * q).floor() + 0.5;
+            // tip of triangle
+            let x_m = (m as f64) + 0.5;
+            // left edge of triangle
+            let x_l = x_m - p1;
+            // right edge of triangle
+            let x_r = x_m + p1;
+            let c = 0.134 + 20.5 / (15.3 + (m as f64));
+            // p1 + area of parallelogram region
+            let p2 = p1 * (1. + 2. * c);
+
+            fn lambda(a: f64) -> f64 {
+                a * (1. + 0.5 * a)
+            }
+
+            let lambda_l = lambda((f_m - x_l) / (f_m - x_l * p));
+            let lambda_r = lambda((x_r - f_m) / (x_r * q));
+            // p1 + area of left tail
+            let p3 = p2 + c / lambda_l;
+            // p1 + area of right tail
+            let p4 = p3 + c / lambda_r;
+
+            // return value
+            let mut y: i64;
+
+            let gen_u = Uniform::new(0., p4);
+            let gen_v = Uniform::new(0., 1.);
+
+            loop {
+                // Step 1: Generate `u` for selecting the region. If region 1 is
+                // selected, generate a triangularly distributed variate.
+                let u = gen_u.sample(rng);
+                let mut v = gen_v.sample(rng);
+                if !(u > p1) {
+                    y = f64_to_i64(x_m - p1 * v + u);
+                    break;
+                }
+
+                if !(u > p2) {
+                    // Step 2: Region 2, parallelograms. Check if region 2 is
+                    // used. If so, generate `y`.
+                    let x = x_l + (u - p1) / c;
+                    v = v * c + 1.0 - (x - x_m).abs() / p1;
+                    if v > 1. {
+                        continue;
+                    } else {
+                        y = f64_to_i64(x);
+                    }
+                } else if !(u > p3) {
+                    // Step 3: Region 3, left exponential tail.
+                    y = f64_to_i64(x_l + v.ln() / lambda_l);
+                    if y < 0 {
+                        continue;
+                    } else {
+                        v *= (u - p2) * lambda_l;
+                    }
+                } else {
+                    // Step 4: Region 4, right exponential tail.
+                    y = f64_to_i64(x_r - v.ln() / lambda_r);
+                    if y > 0 && (y as u64) > self.n {
+                        continue;
+                    } else {
+                        v *= (u - p3) * lambda_r;
+                    }
+                }
+
+                // Step 5: Acceptance/rejection comparison.
+
+                // Step 5.0: Test for appropriate method of evaluating f(y).
+                let k = (y - m).abs();
+                if !(k > SQUEEZE_THRESHOLD && (k as f64) < 0.5 * npq - 1.) {
+                    // Step 5.1: Evaluate f(y) via the recursive relationship. Start the
+                    // search from the mode.
+                    let s = p / q;
+                    let a = s * (n + 1.);
+                    let mut f = 1.0;
+                    if m < y {
+                        let mut i = m;
+                        loop {
+                            i += 1;
+                            f *= a / (i as f64) - s;
+                            if i == y {
+                                break;
+                            }
+                        }
+                    } else if m > y {
+                        let mut i = y;
+                        loop {
+                            i += 1;
+                            f /= a / (i as f64) - s;
+                            if i == m {
+                                break;
+                            }
+                        }
+                    }
+                    if v > f {
+                        continue;
+                    } else {
+                        break;
+                    }
+                }
+
+                // Step 5.2: Squeezing. Check the value of ln(v) againts upper and
+                // lower bound of ln(f(y)).
+                let k = k as f64;
+                let rho = (k / npq) * ((k * (k / 3. + 0.625) + 1./6.) / npq + 0.5);
+                let t = -0.5 * k*k / npq;
+                let alpha = v.ln();
+                if alpha < t - rho {
+                    break;
+                }
+                if alpha > t + rho {
+                    continue;
+                }
+
+                // Step 5.3: Final acceptance/rejection test.
+                let x1 = (y + 1) as f64;
+                let f1 = (m + 1) as f64;
+                let z = (f64_to_i64(n) + 1 - m) as f64;
+                let w = (f64_to_i64(n) - y + 1) as f64;
+
+                fn stirling(a: f64) -> f64 {
+                    let a2 = a * a;
+                    (13860. - (462. - (132. - (99. - 140. / a2) / a2) / a2) / a2) / a / 166320.
+                }
+
+                if alpha > x_m * (f1 / x1).ln()
+                    + (n - (m as f64) + 0.5) * (z / w).ln()
+                    + ((y - m) as f64) * (w * p / (x1 * q)).ln()
+                    // We use the signs from the GSL implementation, which are
+                    // different than the ones in the reference. According to
+                    // the GSL authors, the new signs were verified to be
+                    // correct by one of the original designers of the
+                    // algorithm.
+                    + stirling(f1) + stirling(z) - stirling(x1) - stirling(w)
+                {
+                    continue;
+                }
+
+                break;
+            }
+            assert!(y >= 0);
+            result = y as u64;
+        }
+
+        // Invert the result for p < 0.5.
+        if p != self.p {
+            self.n - result
+        } else {
+            result
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use rand::Rng;
+    use crate::Distribution;
+    use super::Binomial;
+
+    fn test_binomial_mean_and_variance<R: Rng>(n: u64, p: f64, rng: &mut R) {
+        let binomial = Binomial::new(n, p).unwrap();
+
+        let expected_mean = n as f64 * p;
+        let expected_variance = n as f64 * p * (1.0 - p);
+
+        let mut results = [0.0; 1000];
+        for i in results.iter_mut() { *i = binomial.sample(rng) as f64; }
+
+        let mean = results.iter().sum::<f64>() / results.len() as f64;
+        assert!((mean as f64 - expected_mean).abs() < expected_mean / 50.0);
+
+        let variance =
+            results.iter().map(|x| (x - mean) * (x - mean)).sum::<f64>()
+            / results.len() as f64;
+        assert!((variance - expected_variance).abs() < expected_variance / 10.0);
+    }
+
+    #[test]
+    fn test_binomial() {
+        let mut rng = crate::test::rng(351);
+        test_binomial_mean_and_variance(150, 0.1, &mut rng);
+        test_binomial_mean_and_variance(70, 0.6, &mut rng);
+        test_binomial_mean_and_variance(40, 0.5, &mut rng);
+        test_binomial_mean_and_variance(20, 0.7, &mut rng);
+        test_binomial_mean_and_variance(20, 0.5, &mut rng);
+    }
+
+    #[test]
+    fn test_binomial_end_points() {
+        let mut rng = crate::test::rng(352);
+        assert_eq!(rng.sample(Binomial::new(20, 0.0).unwrap()), 0);
+        assert_eq!(rng.sample(Binomial::new(20, 1.0).unwrap()), 20);
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_binomial_invalid_lambda_neg() {
+        Binomial::new(20, -10.0).unwrap();
+    }
+}